A substrate material can be separated into two or more pieces by forming a plurality of laser induced channels along a process path located along an intended line of separation, as taught by Bareman et al. in U.S. Pat. No. 8,842,358. A laser-induced channel edge can be formed upon substrate separation and can have a relatively smooth surface without the need for post-processing operations such as grinding. The types of substrate materials through which such laser-induced channels can be formed has been somewhat limited to substrate materials with a single refractive index.